What does the (P) mean after someones rank? I understand that it means promotable, but what significance does it have?

Nothing. In my experience, Soldiers and officers that write the (P) are insecure. In most cases, they remain in the position of the lower rank.

USAF seems to be the worst about it. Instead of “Major promotable,” they write “Lieutenant Colonel select.” That’s just pompous.

It's a status not a rank.

Attaching tbe (p) to an official signature block can legitimize a decision made by a Soldier of a lower grade that is occupying the slot. For example, some decision may require an O6 signature, but if the approving authority is in promotable status, and is technically still an O5, attaching the - p is used here.

Generally, for most situations, such as a social media site, it is only a source of pride